Waves and Optics
What this domain tests
This domain covers wave properties, superposition, stationary waves, interference, diffraction, refraction, lenses and optical instruments. Practice relates path difference to phase, uses grating and lens equations consistently, and explains fringe patterns through superposition; the chapter does not reproduce a particular examination format.
Core wave relations
- v = fλ; intensity is proportional to amplitude²; polarisation is possible only for transverse waves.
- Phase difference = 2π × (path difference)/λ.
- Superposition: displacements add vectorially. Two identical waves travelling in opposite directions give a stationary wave with nodes every λ/2 and adjacent node–antinode spacing λ/4. No net energy is transported.
- Young's double slit: fringe spacing x = λD/a, where a is the slit separation and D the slit-to-screen distance.
- Diffraction grating: d sinθ = nλ, with d = 1/N and N the number of lines per metre.
Refraction and lenses
Snell's law n₁ sinθ₁ = n₂ sinθ₂; refractive index n = c/v; critical angle sinθc = n₂/n₁ for n₁ > n₂. The special form 1/n applies when the second medium has index approximately one. For lenses use 1/f = 1/u + 1/v with a consistent real-is-positive convention, and signed transverse magnification m = -v/u = image height/object height. For ordinary thin glass lenses in air, a convex lens converges; a concave lens gives a virtual diminished image for a real object.
Worked example
A grating has 500 lines per mm. Find the angle of the second-order maximum for light of wavelength 589 nm.
d = 1/(500 × 1000) = 2.0 × 10⁻⁶ m. sinθ = nλ/d = (2 × 589 × 10⁻⁹)/(2.0 × 10⁻⁶) = 0.589. θ = 36.1°.
Traps that cost marks
- Using degrees inside small-angle formulae that require radians.
- Confusing the order n in d sinθ = nλ with a refractive index.
- Mixing sign conventions in 1/f = 1/u + 1/v, then reporting a virtual image as real.
- Claiming a stationary wave transfers energy along the string.
- Confusing path difference with phase difference (a factor of 2π/λ).
- Forgetting that sinθ ≤ 1 sets a maximum observable order.